A228523 Numbers that are not the product of two Fibonacci numbers (not necessarily distinct).

7, 11, 12, 14, 17, 18, 19, 20, 22, 23, 27, 28, 29, 30, 31, 32, 33, 35, 36, 37, 38, 41, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 56, 57, 58, 59, 60, 61, 62, 66, 67, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 90, 91, 92

Offset

1,1

Comments

All primes except prime Fibonacci numbers are in this sequence.

Links

Table of n, a(n) for n=1..66.

Example

Although 12 can be expressed as a product of Fibonacci numbers, it takes three of them, not two, hence 12 is in the list.
There is no way to express 14 as a product of Fibonacci numbers since its larger prime factor, 7, is not a Fibonacci number, hence 14 is in the list.
16 is not in the list because it can be expressed as 2 * 8.

Mathematica

nn = 12; f = Fibonacci[Range[2, nn]]; f2 = Select[Union[Flatten[Outer[Times, f, f]]], # <= f[[-1]] &]; Complement[Range[f[[-1]]], f2] (* T. D. Noe, Sep 03 2013 *)

Crossrefs

Cf. A049997 (complement).

Sequence in context: A243885 A171017 A195608 * A193301 A213250 A226689

Adjacent sequences: A228520 A228521 A228522 * A228524 A228525 A228526

Keyword

nonn,easy

Author

Alonso del Arte, Sep 02 2013

Status

approved